Joint USYD-UNSW Seminar on Stochastic PDEs: Emanuela Gussetti (Bielefeld University) -- Existence of statistical stationary solutions to the Schrodinger Map Equation in 1D

This is a zoom only seminar: https://unsw.zoom.us/j/83425275881?from=addon Meeting ID:
83425275881 Password: 041345 

In this talk, we discuss the existence of statistically stationary solutions to the
Schrodinger map equation on a one-dimensional domain, with null Neumann boundary
conditions, or on the one-dimensional torus.  To approximate the Schrodinger map
equation, we employ the stochastic Landau-Lifschitz-Gilbert equation.  By a limiting
procedure a la Kuksin, we establish existence of a random initial datum, whose
distribution is preserved under the dynamic of the deterministic equation.  We explore
the relationship between the Schrödinger map equation, the binormal curvature flow and
the cubic non-linear Schrodinger equation.  Additionally, we prove existence of
statistically stationary solutions to the binormal curvature flow.  This is a joint work
with M.  Hofmanova (https://arxiv.org/abs/2501.16499).